SEPTEMBER 20, 1918] 
proximately proportional to the mathematical 
output of the periods covered. In Chart IL. 
letting a short ordinate represent the average 
annual mathematical production during the 
first period extending from antiquity to 1200 
Ave rage Annual Production, 
1200-1668 
(668-172 
2000BC.~ /200A.D, 
A.D., we find that the average yearly production 
for the second period of 468 years is 6.9 times 
greater than for the first period, and for the 
third period of 90 years, 35.3 times greater. 
It will be convenient to take the average an- 
nual output during the first period as a unit 
measure of mathematical production. Accord- 
ingly, the figures for the first three periods are 
per annum, respectively, 1, 6.9, 35.3. 
That we may graph more conveniently the 
expansion of mathematical literature since 
1758, the third period is represented in Chart 
II. by a short ordinate. The fourth period of 
41 years shows that the annual publications 
are 2.7 times more voluminous than those of 
the third period, indicating a yearly produc- 
tion of 95.8. To carry the comparison down 
to later periods I counted the number of 
mathematical writers given in the first two 
volumes of Poggendorff’s “ Handwérterbuch ” 
for the eleven years 1790-1800. I found this 
SCIENCE 
281 
number to be 244. For the period 1830-1840 I 
obtained 341 names. This indicates an in- 
crease in the ratio 1.398. I also counted the 
number of lines taken up in the enumeration 
of titles of books and articles of 134 mathe- 
matical writers for 1790-1800 and of 134 
mathematical writers for 1830-1840. I began 
at random with the name of Jolly and in 
succession took the names of mathematical 
authors who wrote during these intervals. By 
this test the average productiveness of the 
individuals of these two groups proved, to my 
surprise, to be nearly the same; it was in the 
ratio of 1:1.04 in favor of the later group. 
Chart Zz. 
Aver age Annual Pa advetion. 
1668-(758 
17 58-1797. 1799-18 FS, 18 35-1875, (875-190) 
Combining the ratios of 1.398 and 1.04 I get 
1.45 as the rate of increase in volume of 
mathematical literature of the period 1830- 
1840 over that of 1790-1800. The gradient 
fixed by the middle points of the third and 
fourth periods in Chart II. indicates for 1799 
an approximate production of 114.4. Maulti- 
plying 114.4 by 1.45 gives 165.9 as the produc- 
tion for the year 1835. The average of 114.4 
and 165.9, or 140.1 is the average annual pro- 
duction during the fifth period. 
For the eleven years 1870-1880 I found in 
the third volume of Poggendorff 888 names 
